Well, you should. Pigeons can have an illness or fights that make them loose some toes and because of this, they can walk slowly or not react as fast as the others. One day I saw one on the street while a truck was comming fast towards it. I heard pretty clear a "plop" sound, like the sound of a bag exploding. I just hear it because I didn't want to look at it. It's not the kind of image you want to remember.
I still remember seeing a bird die when I was a small child. The bird was in the street right next to an intersection, and a car made a right turn at the intersection and caught the bird unaware.